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Reservoir-triggered seismicity has been observed near dams during construction, impoundment, and cyclic filling in many parts of the earth. In Turkey, the number of dams has increased substantially over the last decade, with Ataturk Dam being the largest dam in Turkey with a total water capacity of 48.7 billion m(3). After the construction of the dam, the monitoring network has improved. Considering earthquakes above the long-term completeness magnitude of M-C = 3.5, the local seismicity rate has substantially increased after the filling of the reservoir. Recently, two damaging earthquakes of M-w 5.5 and M-w 5.1 occurred in the town of Samsat near the Ataturk Reservoir in 2017 and 2018, respectively. In this study, we analyze the spatio-temporal evolution of seismicity and its source properties in relation to the temporal water-level variations and the stresses resulting from surface loading and pore-pressure diffusion. We find that water-level and seismicity rate are anti-correlated, which is explained by the stabilization effect of the gravitational induced stress imposed by water loading on the local faults. On the other hand, we find that the overall effective stress in the seismogenic zone increased over decades due to pore-pressure diffusion, explaining the enhanced background seismicity during recent years. Additionally, we observe a progressive decrease of the Gutenberg-Richter b-value. Our results indicate that the stressing rate finally focused on the region where the two damaging earthquakes occurred in 2017 and 2018.
The Alpine mountains in central Europe are characterized by a heterogeneous crust accumulating different tectonic units and blocks in close proximity to sedimentary foreland basins. Centroid moment tensor inversion provides insight into the faulting mechanisms of earthquakes and related tectonic processes but is significantly aggravated in such an environment. Thanks to the dense AlpArray seismic network and our flexible bootstrap-based inversion tool Grond, we are able to test different setups with respect to the uncertainties of the obtained moment tensors and centroid locations. We evaluate the influence of frequency bands, azimuthal gaps, input data types, and distance ranges and study the occurrence and reliability of non-double-couple (DC) components. We infer that for most earthquakes (M-w >= 3.3) a combination of time domain full waveforms and frequency domain amplitude spectra in a frequency band of 0.02-0.07 Hz is suitable. Relying on the results of our methodological tests, we perform deviatoric moment tensor (MT) inversions for events with M-w > 3.0. Here, we present 75 solutions for earthquakes between January 2016 and December 2019 and analyze our results in the seismotectonic context of historical earthquakes, seismic activity of the last 3 decades, and GNSS deformation data. We study regions of comparably high seismic activity during the last decades, namely the Western Alps, the region around Lake Garda, and the eastern Southern Alps, as well as clusters further from the study region, i.e., in the northern Dinarides and the Apennines. Seismicity is particularly low in the Eastern Alps and in parts of the Central Alps. We apply a clustering algorithm to focal mechanisms, considering additional mechanisms from existing catalogs. Related to the N-S compressional regime, E-W-to-ENE-WSW-striking thrust faulting is mainly observed in the Friuli area in the eastern Southern Alps. Strike-slip faulting with a similarly oriented pressure axis is observed along the northern margin of the Central Alps and in the northern Dinarides. NW-SE-striking normal faulting is observed in the NW Alps, showing a similar strike direction to normal faulting earthquakes in the Apennines. Both our centroid depths and hypocentral depths in existing catalogs indicate that Alpine seismicity is predominantly very shallow; about 80% of the studied events have depths shallower than 10 km.
With the present study, we introduce a fast and robust method to calculate the source displacement spectra of small earthquakes on a local to regional scale. The work is based on the publicly available Qopen method of full envelope inversion, which is further tuned for the given purpose. Important source parameters-seismic moment, moment magnitude, corner frequency, and high-frequency fall off-are determined from the source spectra by fitting a simple earthquake source model. The method is demonstrated by means of a data set comprising the 2018 West Bohemia earthquake swarm. We report moment magnitudes, corner frequencies, and centroid moment tensors inverted from short-period body waves with the Grond package for all earthquakes with a local magnitude larger than 1.8. Moment magnitudes calculated by envelope inversion show a very good agreement to moment magnitudes resulting from the probabilisitc moment tensor inversion. Furthermore, source displacement spectra from envelope inversion show a good agreement with spectra obtained by multiple taper analysis of the direct onsets of body waves but are not affected by the large scatter of the second. The seismic moments obtained with the envelope inversion scale with corner frequencies according to M-0 proportional to f(c)(-4.7). Earthquakes of the present data set result in a smaller stress drop for smaller magnitudes. Self-similarity of earthquake rupture is not observed. In addition, we report frequency-dependent site amplification at the used stations.
We examine sub-caldera structure and seismicity in and around the Okataina Volcanic Centre (OVC), Taupo Volcanic Zone, New Zealand, using seismic data collected over 4+ years with a temporary array of broadband and short-period seismometers, supplementing data from the permanent New Zealand seismometer network.
We derive a new 3-D image of P-wave seismic velocity for the upper crust in the region, using double-difference seismic tomography and utilising waveform cross-correlations. We subsequently relocate 6989 earthquakes which occurred in the region over the 2010-2021 time period, using the 3D velocity model.
The seismicity distribution shows spatial clusters west of Lake Rotomahana, as well as beneath Haroharo and the Makatiti Dome, inside the Okataina caldera. Beneath Makatiti Dome 90% of the events are shallower than 7.7 +/- 0.5 km.
Outside of the Okataina caldera event relocations highlight short (similar to 3-4 km long) streaks of activity in the Ngakuru graben, part of the active Taupo Rift southwest of Okataina caldera. Inside the OVC the relocated seismicity beneath Makatiti appears closely associated with low (similar to 10%) P-wave velocity anomalies, which we resolve in the similar to 5-to-8-km depth range beneath the Okataina caldera, and which are likely related to partial melt and/or fluid-volatile pathways.
Moment tensor analyses for two larger-magnitude events (M(L)4.5 and M(L)4.9) near Haroharo indicate normal faulting, with NNE-SSW fault strike, but with positive CLVD and positive isotropic components when allowing for a full moment tensor, consistent with a magmatic environment with degassing and/or fluid migration.
Understanding and constraining the source of geodetic deformation in volcanic areas is an important component of hazard assessment. Here, we analyse deformation and seismicity for one year before the March 2021 Fagradalsfjall eruption in Iceland. We generate a high-resolution catalogue of 39,500 earthquakes using optical cable recordings and develop a poroelastic model to describe three pre-eruptional uplift and subsidence cycles at the Svartsengi geothermal field, 8 km west of the eruption site. We find the observed deformation is best explained by cyclic intrusions into a permeable aquifer by a fluid injected at 4 km depth below the geothermal field, with a total volume of 0.11 ± 0.05 km3 and a density of 850 ± 350 kg m–3. We therefore suggest that ingression of magmatic CO2 can explain the geodetic, gravity and seismic data, although some contribution of magma cannot be excluded.
An earthquake swarm affected the Bransfield Strait, Antarctica, a unique rift basin in transition from intra-arc rifting to ocean spreading. The swarm, counting similar to 85,000 volcano-tectonic earthquakes since August 2020, is located close to the Orca submarine volcano, previously considered inactive. Simultaneously, geodetic data reported up to similar to 11 cm north-westward displacement over King George Island. We use a broad variety of geophysical data and methods to reveal the complex migration of seismicity, accompanying the intrusion of 0.26-0.56 km(3) of magma. Strike-slip earthquakes mark the intrusion at depth, while shallower normal faulting the similar to 20 km long lateral growth of a dike. Seismicity abruptly decreased after a Mw 6.0 earthquake, suggesting the magmatic dike lost pressure with the slipping of a large fault. A seafloor eruption is likely, but not confirmed by sea surface temperature anomalies. The unrest documents episodic magmatic intrusion in the Bransfield Strait, providing unique insights into active continental rifting.
The investigation of stresses, faults, structure and seismic hazards requires a good understanding and mapping of earthquake rupture and slip. Constraining the finite source of earthquakes from seismic and geodetic waveforms is challenging because the directional effects of the rupture itself are small and dynamic numerical solutions often include a large number of free parameters. The computational effort is large and therefore difficult to use in an exploratory forward modelling or inversion approach. Here, we use a simplified self-similar fracture model with only a few parameters, where the propagation of the fracture front is decoupled from the calculation of the slip. The approximative method is flexible and computationally efficient. We discuss the strengths and limitations of the model with real-case examples of well-studied earthquakes. These include the M-w 8.3 2015 Illapel, Chile, megathrust earthquake at the plate interface of a subduction zone and examples of continental intraplate strike-slip earthquakes like the M-w 7.1 2016 Kumamoto, Japan, multisegment variable slip event or the M-w 7.5 2018 Palu, Indonesia, supershear earthquake. Despite the simplicity of the model, a large number of observational features ranging from different rupture-front isochrones and slip distributions to directional waveform effects or high slip patches are easy to model. The temporal evolution of slip rate and rise time are derived from the incremental growth of the rupture and the stress drop without imposing other constraints. The new model is fast and implemented in the open-source Python seismology toolbox Pyrocko, ready to study the physics of rupture and to be used in finite source inversions.
Despite its high-seismogenic potential, the details of the seismogenic processes of Zagros Simply Folded Belt (SFB) remains debated. Three large earthquakes (M-w 7.3, 5.9 and 6.3) struck in the Lurestan arc of the Zagros SFB in 2017 and 2018. The sequence was recorded by seismic stations at regional, and teleseismic distances. Coseismic surface displacements, measured by Sentinel-1A/B satellites, provide additional data and a unique opportunity to study these earthquakes in detail. Here, we complement previous studies of the coseismic slip distribution of the 12 November 2017 M-w 7.3 Ezgeleh earthquake by a detailed analysis of its aftershocks, and we analysed the rupture process of the two interrelated earthquakes (25 August 2018 M-w 5.9 Tazehabad and the 25 November 2018 M-w 6.3 Sarpol-e Zahab earthquakes). We model the surface displacements obtained from Interferometric Synthetic Aperture Radar (InSAR) measurements and seismic records. We conduct non-linear probabilistic optimizations based on joint InSAR and seismic data to obtain finite-fault rupture of these earthquakes. The Lurestan arc earthquakes were followed by a sustained aftershock activity, with 133 aftershocks exceeding M-n 4.0 until 30 December 2019. We rely on the permanent seismic networks of Iran and Iraq to relocate similar to 700 M-n 3 + events and estimate moment tensor solutions for 85 aftershocks down to M-w 4.0. The 2017 Ezgeleh earthquake has been considered to activate a low-angle (similar to 17 degrees) dextral-thrust fault at the depth of 10-20 km. However, most of its aftershocks have shallow centroid depths (8-12 km). The joint interpretation of finite source models, moment tensor and hypocentral location indicate that the 2018 Tazehabad and Sarpol-e Zahab earthquakes ruptured different strike-slip structures, providing evidence for the activation of the sinistral and dextral strike-slip faults, respectively. The deformation in the Lurestan arc is seismically accommodated by a complex fault system involving both thrust and strike-slip faults. Knowledge about the deformation characteristics is important for the understanding of crustal shortening, faulting and hazard and risk assessment in this region.
Data recorded by distributed acoustic sensing (DAS) along an optical fibre sample the spatial and temporal properties of seismic wavefields at high spatial density. Often leading to massive amount of data when collected for seismic monitoring along many kilometre long cables. The spatially coherent signals from weak seismic arrivals within the data are often obscured by incoherent noise. We present a flexible and computationally efficient filtering technique, which makes use of the dense spatial and temporal sampling of the data and that can handle the large amount of data. The presented adaptive frequency-wavenumber filter suppresses the incoherent seismic noise while amplifying the coherent wavefield. We analyse the response of the filter in time and spectral domain, and we demonstrate its performance on a noisy data set that was recorded in a vertical borehole observatory showing active and passive seismic phase arrivals. Lastly, we present a performant open-source software implementation enabling real-time filtering of large DAS data sets.
Full-waveform-based characterization of acoustic emission activity in a mine-scale experiment
(2020)
Understanding fracturing processes and the hydromechanical relation to induced seismicity is a key question for enhanced geothermal systems (EGS). Commonly massive fluid injection, predominately causing hydroshearing, are used in large-scale EGS but also hydraulic fracturing approaches were discussed. To evaluate the applicability of hydraulic fracturing techniques in EGS, six in situ, multistage hydraulic fracturing experiments with three different injection schemes were performed under controlled conditions in crystalline rock at the Aspo Hard Rock Laboratory (Sweden). During the experiments the near-field ground motion was continuously recorded by 11 piezoelectric borehole sensors with a sampling rate of 1 MHz. The sensor network covered a volume of 30x30x30 m around a horizontal, 28-m-long injection borehole at a depth of 410 m. To extract and characterize massive, induced, high-frequency acoustic emission (AE) activity from continuous recordings, a semi-automated workflow was developed relying on full waveform based detection, classification and location procedures. The approach extended the AE catalogue from 196 triggered events in previous studies to more than 19600 located AEs. The enhanced catalogue, for the first time, allows a detailed analysis of induced seismicity during single hydraulic fracturing experiments, including the individual fracturing stages and the comparison between injection schemes. Beside the detailed study of the spatio-temporal patterns, event clusters and the growth of seismic clouds, we estimate relative magnitudes and b-values of AEs for conventional, cyclic progressive and dynamic pulse injection schemes, the latter two being fatigue hydraulic fracturing techniques. While the conventional fracturing leads to AE patterns clustered in planar regions, indicating the generation of a single main fracture plane, the cyclic progressive injection scheme results in a more diffuse, cloud-like AE distribution, indicating the activation of a more complex fracture network. For a given amount of hydraulic energy (pressure multiplied by injected volume) pumped into the system, the cyclic progressive scheme is characterized by a lower rate of seismicity, lower maximum magnitudes and significantly larger b-values, implying an increased number of small events relative to the large ones. To our knowledge, this is the first direct comparison of high resolution seismicity in a mine-scale experiment induced by different hydraulic fracturing schemes.
Earthquake source arrays
(2020)
A collection of earthquake sources recorded at a single station, under specific conditions, are considered as a source array (SA), that is interpreted as if earthquake sources originate at the station location and are recorded at the source location. Then, array processing methods, that is array beamforming, are applicable to analyse the recorded signals. A possible application is to use source array multiple event techniques to locate and characterize near-source scatterers and structural interfaces. In this work the aim is to facilitate the use of earthquake source arrays by presenting an automatic search algorithm to configure the source array elements. We developed a procedure to search for an optimal source array element distribution given an earthquake catalogue including accurate origin time and hypocentre locations. The objective function of the optimization process can be flexibly defined for each application to ensure the prerequisites (criteria) of making a source array. We formulated four quantitative criteria as subfunctions and used the weighted sum technique to combine them in one single scalar function. The criteria are: (1) to control the accuracy of the slowness vector estimation using the time domain beamforming method, (2) to measure the waveform coherency of the array elements, (3) to select events with lower location error and (4) to select traces with high energy of specific phases, that is, sp- or ps-phases. The proposed procedure is verified using synthetic data as well as real examples for the Vogtland region in Northwest Bohemia. We discussed the possible application of the optimized source arrays to identify the location of scatterers in the velocity model by presenting a synthetic test and an example using real waveforms.
Earthquakes often rupture across more than one fault segment. If such rupture segmentation occurs on a significant scale, a simple point-source or one-fault model may not represent the rupture process well. As a consequence earthquake characteristics inferred, based on one-source assumptions, may become systematically wrong. This might have effects on follow-up analyses, for example regional stress field inversions and seismic hazard assessments. While rupture segmentation is evident for most M-w > 7 earthquakes, also smaller ones with 5.5 < M-w < 7 can be segmented. We investigate the sensitivity of globally available data sets to rupture segmentation and their resolution to reliably estimate the mechanisms in presence of segmentation. We focus on the sensitivity of InSAR (Interferometric Synthetic Aperture Radar) data in the static near-field and seismic waveforms in the far-field of the rupture and carry out non-linear and Bayesian optimizations of single-source and two-sources kinematic models (double-couple point sources and finite, rectangular sources) using InSAR and teleseismic waveforms separately. Our case studies comprises of four M-w 6-7 earthquakes: the 2009 L'Aquila and 2016 Amatrice (Italy) and the 2005 and 2008 Zhongba (Tibet) earthquakes. We contrast the data misfits of different source complexity by using the Akaike informational criterion (AIC). We find that the AIC method is well suited for data-driven inferences on significant rupture segmentation for the given data sets. This is based on our observation that an AIC-stated significant improvement of data fit for two-segment models over one-segment models correlates with significantly different mechanisms of the two source segments and their average compared to the single-segment mechanism. We attribute these modelled differences to a sufficient sensitivity of the data to resolve rupture segmentation. Our results show that near-field data are generally more sensitive to rupture segmentation of shallow earthquakes than far-field data but that also teleseismic data can resolve rupture segmentation in the studied magnitude range. We further conclude that a significant difference in the modelled source mechanisms for different segmentations shows that an appropriate choice of model segmentation matters for a robust estimation of source mechanisms. It reduces systematic biases and trade-off and thereby improves the knowledge on the rupture. Our study presents a strategy and method to detect significant rupture segmentation such that an appropriate model complexity can be used in the source mechanism inference. A similar, systematic investigation of earthquakes in the range of M-w 5.5-7 could provide important hazard-relevant statistics on rupture segmentation. In these cases single-source models introduce a systematic bias. Consideration of rupture segmentation therefore matters for a robust estimation of source mechanisms of the studied earthquakes.
The Quaternary volcanic fields of the Eifel (Rhineland-Palatinate, Germany) had their last eruptions less than 13,000 years ago. Recently, deep low-frequency (DLF) earthquakes were detected beneath one of the volcanic fields showing evidence of ongoing magmatic activity in the lower crust and upper mantle. In this work, seismic wide- and steep-angle experiments from 1978/1979 and 1987/1988 are compiled, partially reprocessed and interpreted, together with other data to better determine the location, size, shape, and state of magmatic reservoirs in the Eifel region near the crust-mantle boundary. We discuss seismic evidence for a low-velocity gradient layer from 30-36 km depth, which has developed over a large region under all Quaternary volcanic fields of the Rhenish Massif and can be explained by the presence of partial melts. We show that the DLF earthquakes connect the postulated upper mantle reservoir with the upper crust at a depth of about 8 km, directly below one of the youngest phonolitic volcanic centers in the Eifel, where CO(2)originating from the mantle is massively outgassing. A bright spot in the West Eifel between 6 and 10 km depth represents a Tertiary magma reservoir and is seen as a model for a differentiated reservoir beneath the young phonolitic center today. We find that the distribution of volcanic fields is controlled by the Variscan lithospheric structures and terrane boundaries as a whole, which is reflected by an offset of the Moho depth, a wedge-shaped transparent zone in the lower crust and the system of thrusts over about 120 km length.
Global earthquake locations are often associated with very large systematic travel-time residuals even for clear arrivals, especially for regional and near-regional stations in subduction zones because of their strongly heterogeneous velocity structure. Travel-time corrections can drastically reduce travel-time residuals at regional stations and, in consequence, improve the relative location accuracy. We have extended the shrinking-box source-specific station terms technique to regional and teleseismic distances and adopted the algorithm for probabilistic, nonlinear, global-search location. We evaluated the potential of the method to compute precise relative hypocentre locations on a global scale. The method has been applied to two specific test regions using existing P- and pP-phase picks. The first data set consists of 3103 events along the Chilean margin and the second one comprises 1680 earthquakes in the Tonga-Fiji subduction zone. Pick data were obtained from the GEOFON earthquake bulletin, produced using data from all available, global station networks. A set of timing corrections varying as a function of source position was calculated for each seismic station. In this way, we could correct the systematic errors introduced into the locations by the inaccuracies in the assumed velocity structure without explicitly solving for a velocity model. Residual statistics show that the median absolute deviation of the travel-time residuals is reduced by 40-60 per cent at regional distances, where the velocity anomalies are strong. Moreover, the spread of the travel-time residuals decreased by similar to 20 per cent at teleseismic distances (>28 degrees). Furthermore, strong variations in initial residuals as a function of recording distance are smoothed out in the final residuals. The relocated catalogues exhibit less scattered locations in depth and sharper images of the seismicity associated with the subducting slabs. Comparison with a high-resolution local catalogue reveals that our relocation process significantly improves the hypocentre locations compared to standard locations.
Two nuclear explosions were carried out by the Democratic People’s Republic of North Korea in January and September 2016. Epicenters were located close to those of the 2006, 2009, and 2013 previous explosions. We perform a seismological analysis of the 2016 events combining the analysis of full waveforms at regional distances and seismic array beams at teleseismic distances. We estimate the most relevant source parameters, such as source depth, moment release, and full moment tensor (MT). The best MT solution can be decomposed into an isotropic source, directly related with the explosion and an additional deviatoric term, likely due to near‐source interactions with topographic and/or underground facilities features. We additionally perform an accurate resolution test to assess source parameters uncertainties and trade‐offs. This analysis sheds light on source parameters inconsistencies among studies on previous shallow explosive sources. The resolution of the true MT is hindered by strong source parameters trade‐offs, so that a broad range of well‐fitting MT solutions can be found, spanning from a dominant positive isotropic term to a dominant negative vertical compensated linear vector dipole. The true mechanism can be discriminated by additionally modeling first‐motion polarities at seismic arrays at teleseismic distances. A comparative assessment of the 2016 explosion with earlier nuclear tests documents similar vertical waveforms but a significant increase of amplitude for the 2016 explosions, which proves that the 9 September 2016 was the largest nuclear explosion ever performed in North Korea with a magnitude Mw 4.9 and a shallow depth of less than 2 km, although there are no proofs of a fusion explosion. Modeling transversal component waveforms suggests variable size and orientation of the double‐couple components of the 2009, 2013, and 2016 sources.
On April 29, 2017 at 0:56 UTC (2:56 local time), an M (W) = 2.8 earthquake struck the metropolitan area between Leipzig and Halle, Germany, near the small town of Markranstadt. The earthquake was felt within 50 km from the epicenter and reached a local intensity of I (0) = IV. Already in 2015 and only 15 km northwest of the epicenter, a M (W) = 3.2 earthquake struck the area with a similar large felt radius and I (0) = IV. More than 1.1 million people live in the region, and the unusual occurrence of the two earthquakes led to public attention, because the tectonic activity is unclear and induced earthquakes have occurred in neighboring regions. Historical earthquakes south of Leipzig had estimated magnitudes up to M (W) ae 5 and coincide with NW-SE striking crustal basement faults. We use different seismological methods to analyze the two recent earthquakes and discuss them in the context of the known tectonic structures and historical seismicity. Novel stochastic full waveform simulation and inversion approaches are adapted for the application to weak, local earthquakes, to analyze mechanisms and ground motions and their relation to observed intensities. We find NW-SE striking normal faulting mechanisms for both earthquakes and centroid depths of 26 and 29 km. The earthquakes are located where faults with large vertical offsets of several hundred meters and Hercynian strike have developed since the Mesozoic. We use a stochastic full waveform simulation to explain the local peak ground velocities and calibrate the method to simulate intensities. Since the area is densely populated and has sensitive infrastructure, we simulate scenarios assuming that a 12-km long fault segment between the two recent earthquakes is ruptured and study the impact of rupture parameters on ground motions and expected damage.
The occurrence of deep low-frequency (DLF) microearthquakes beneath volcanoes is commonly attributed to mass transport in the volcanic plumbing system and used to infer feeding channels from and into magma reservoirs. The key question is how magmas migrate from depth to the shallow crust and whether magma reservoirs are currently being recharged. For the first time since the improvement of the local seismic networks in the East Eifel region (Rhineland-Palatinate, Germany), we detect and locate recurrent DLF earthquakes in the lower crust and upper mantle beneath the Laacher See Volcano (LSV), using a joint data set of permanent sensors and a temporary deployment. So far, eight DLF earthquake sequences were observed in four distinct clusters between 10 and 40 km depth. These clusters of weak events (M-L< 2) align along an approximately 80. southeast dipping line south of the LSV. Moment tensor solutions of these events have large shear components, and the irregular dispersion and long coda of body waves indicate interaction processes between shear cracks and fluids. We find a rotation of P-axes orientation for shallow tectonic earthquakes compared to DLF events, indicating that the stress field in the depth interval of DLF events might favour a vertical migration of magma or magmatic fluids. The caldera of the LSV was formed by the last major eruption of the East Eifel Volcanic Field only 12.9 kyr ago, fed by a shallow magma chamber at 5-8 km depth and erupting a total magma volume of 6.7 km(3). The observed DLF earthquake activity and continuous volcanic gas emissions around the LSV indicate an active magmatic system, possibly connected with an upper mantle melt zone.
The design of an array configuration is an important task in array seismology during experiment planning. Often the array response function (ARF), which depends on the relative position of array stations and frequency content of the incoming signals, is used as the array design criterion. In practice, additional constraints and parameters have to be taken into account, for example, land ownership, site-specific noise levels or characteristics of the seismic sources under investigation. In this study, a flexible array design framework is introduced that implements a customizable scenario modelling and optimization scheme by making use of synthetic seismograms. Using synthetic seismograms to evaluate array performance makes it possible to consider additional constraints. We suggest to use synthetic array beamforming as an array design criterion instead of the ARF. The objective function of the optimization scheme is defined according to the monitoring goals, and may consist of a number of subfunctions. The array design framework is exemplified by designing a seven-station small-scale array to monitor earthquake swarm activity in Northwest Bohemia/Vogtland in central Europe. Two subfunctions are introduced to verify the accuracy of horizontal slowness estimation; one to suppress aliasing effects due to possible secondary lobes of synthetic array beamforming calculated in horizontal slowness space and the other to reduce the event’s mislocation caused by miscalculation of the horizontal slowness vector. Subsequently, a weighting technique is applied to combine the subfunctions into one single scalar objective function to use in the optimization process.
The computation of such synthetic GFs is computationally and operationally demanding. As a consequence, the onthe-fly recalculation of synthetic GFs in each iteration of an optimisation is time-consuming and impractical. Therefore, the pre-calculation and efficient storage of synthetic GFs on a dense grid of source to receiver combinations enables the efficient lookup and utilisation of GFs in time-critical scenarios. We present a Python-based framework and toolkit - Pyrocko-GF - that enables the pre-calculation of synthetic GF stores, which are independent of their numerical calculation method and GF transfer function. The framework aids in the creation of such GF stores by interfacing a suite of established numerical forward modelling codes in seismology (computational back ends). So far, interfaces to back ends for layered Earth model cases have been provided; however, the architecture of Pyrocko-GF is designed to cover back ends for other geometries (e.g. full 3-D heterogeneous media) and other physical quantities (e.g. gravity, pressure, tilt). Therefore, Pyrocko-GF defines an extensible GF storage format suitable for a wide range of GF types, especially handling elasticity and wave propagation problems. The framework assists with visualisations, quality control, and the exchange of GF stores, which is supported through an online platform that provides many pre-calculated GF stores for local, regional, and global studies. The Pyrocko-GF toolkit comes with a well-documented application programming interface (API) for the Python programming language to efficiently facilitate forward modelling of geophysical processes, e.g. synthetic waveforms or static displacements for a wide range of source models.